I just published a book on amazon for kindle, I downloaded a sample on to my win 8 phone, and it looks all wonky. It is still readable but somethings just look unformatted and some icons don't resize when their suppose to. When I download the mobi file from KDP to view it on my kindle previewer everything looks and is working just fine.

Do people have any grounds for complaining if the e-book doesn't look formatted on a non kindle device while purchasing it from amazon which states it is a Kindle Edition?

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This is my first published E-book.

Also I notice in the table of contents preview on the amazon website some of my links appear to be not working when in fact they do when I download it and view it on kindle previewer.

A. If you have a Kindle app on your Iphone, Windows phone or Android phone the book should be fine.
B. If for any reason someone doesn't like the book they have seven days to return it, no questions asked.
C. In my opinion, you have no problem but I'm not a lawyer.
D. I am assuming your question is legitimate and not simply a way to try and get people to look at your book.

Of course people have a right to complain if the book looks like cr*p on one of the apps. Did you perhaps try to over-control the formatting? Keep in mind that everything has to reflow, so tight control of formatting is not possible.

I do notice a couple of non-links in the TOC in the Look Inside view. Make sure your start and end tags are correct. You might want to run it through an HTML validator to double-check. There are dozens of free ones online.

when I say icons I mean images. For my image sizes I entered them in as pecetages and when I go through the different viewers on kindle previewer the images re adjust but when I check it out on my phone via the kindle app some things that are suppose to have their own page don't and some images appear way too big